When you sent Bittrex (or send any exchange) your Monero, you should always check two things.
1. Do they have an integrated Monero Address (Monero address would be 106 characters)
2. Do they have a payment ID (Monero address would be 95 characters)
A payment ID links a payment to the owner.
An integrated Monero address hashes the payment ID.
Without this, an exchange can't link your payment to you, especially since Monero is a privacy coin.